相关论文: A quantum tug of war between randomness and symmet…
The peculiar uncertainty or randomness of quantum measurements stems from coherence, whose information-theoretic characterization is currently under investigation. Under the resource theory of coherence, it is interesting to investigate…
We investigate the generic aspects of quantum coherence guided by the concentration of measure phenomenon. We find the average relative entropy of coherence of pure quantum states sampled randomly from the uniform Haar measure and show that…
Symmetries are a key concept to connect mathematical elegance with physical insight. We consider measurement assemblages in quantum mechanics and show how their symmetry can be described by means of the so-called discrete bundles. It turns…
This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
The concept of randomness in quantum computing has been central to construct benchmarking tools, cryptographic protocols, as well as a proof of beyond classical computation. Discerning whether quantum states (or unitaries) are randomly…
We introduce a way of quantifying how informative a quantum measurement is, starting from a resource-theoretic perspective. This quantifier, which we call the robustness of measurement, describes how much `noise' must be added to a…
We consider a generalized model of repeated quantum interactions, where a system $\mathcal{H}$ is interacting in a random way with a sequence of independent quantum systems $\mathcal{K}_n, n \geq 1$. Two types of randomness are studied in…
In this paper, we detail an orthogonalization procedure that allows for the quantification of the amount of coherence present an arbitrary superposition of coherent states. The present construction is based on the quantum coherence resource…
Quantum measurements can produce randomness arising from the uncertainty principle. When measuring a state with von Neumann measurements, the intrinsic randomness can be quantified by the quantum coherence of the state on the measurement…
Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian…
A symmetry of a state $\vert \psi \rangle$ is a unitary operator of which $\vert \psi \rangle$ is an eigenvector. When $\vert \psi \rangle$ is an unknown state supplied by a black-box oracle, the state's symmetries provide key physical…
Information scrambling, the process by which quantum information spreads and becomes effectively inaccessible, is central to modern quantum statistical physics and quantum chaos. These lecture notes provide an introduction to information…
Given a preferred orthonormal basis $B$ in the Hilbert space of a quantum system we define a measure of the coherence generating power of a unitary operation with respect to $B$. This measure is the average coherence generated by the…
Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian…
Measurements with randomly chosen settings determine many important properties of quantum states without the need for a shared reference frame or calibration. They naturally emerge in the context of quantum communication and quantum…
As random operations for quantum systems are intensively used in various quantum information tasks, a trustworthy measure of the randomness in quantum operations is highly demanded. The Haar measure of randomness is a useful tool with wide…
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…
Quantum state designs, by enabling an efficient sampling of random quantum states, play a quintessential role in devising and benchmarking various quantum protocols with broad applications ranging from circuit designs to black hole physics.…
The emergence of randomness from unitary quantum dynamics is a central problem across diverse disciplines, ranging from the foundations of statistical mechanics to quantum algorithms and quantum computation. Physical systems are invariably…
The operational meaning of coherence measure lies at very heart of the coherence theory. In this paper, we provide an operational interpretation for geometric coherence, by proving that the geometric coherence of a quantum state is equal to…